I thought barrel rolls were worth 1500 points. But I guess I was wrong.
Anyway, to perform a barrel roll (BR), just press left-right-left or right-left-right when your ship is airborne. On some tracks, this is very hard to do because there aren't many places where you can go airborne (like Moa Therma reverse). On other tracks, there are many opportunities for BRs (like Sebenco Climb). I have found it harder to perform BRs in zone mode because the ships seem more glued to the track.
Be advised that all BRs consume 15 ship energy points in zone and regular racing. Even if your BR is unsuccessful (meaning your ship doesn't roll completely because you hit the ground), you still lose the 15 ship energy points and you don't get the 1000 (or 1500?) point bonus. In zone mode, BRs are a great way to increase your score, but only attempt them if you can score perfect zones. Clearing perfect zones are the only way you can restore your ship energy in zone mode.
Good luck, and happy zoning! We need more zone pilots here!